The IS-K, a local affiliate of the Islamic State terror group in Afghanistan, had claimed responsibility for the attack.
As for the bombers and gunmen involved, he said, "We have some reason to believe we know who they are ... not certain. He said he had instructed military commanders to develop plans to strike IS assets, leadership and facilities.
About 5,000 US troops have been deployed in Kabul airport to help with the airlift process.
The situation in Afghanistan worsened further on Sunday, as Kabul was taken over by the Taliban.
There was chaos and confusion at the Kabul airport as thousands of Afghans crowded the tarmac trying to catch a flight out of Afghanistan.